PerfectNumbers

function factorize( item, target, arr ){
    try{
        if( ( typeof target === "undefined" || target === null ) && !Array.isArray(arr) ){
            return factorize(parseInt(item), Math.ceil(Math.sqrt(parseInt(item))), [parseInt(item)]);
        } else{ 
            if( target > 0 ){
                if( item % target === 0 ){
                    arr.push(target);
                    arr.push(item/target);
                }
                return factorize(item,parseInt(target-1),arr);
            } else {
                return Object.keys(arr.reduce((map,item)=>{map[item]=item;return map;},{})).map(item=>parseInt(item));
            }
        }
    } catch(error){
        return [-1];
    }
    return [-1];
}

function sumFactors( factors ){
    if( Array.isArray(factors) && factors.length > 1 ){
        return factors.slice(0,factors.length-1).reduce((sum,item)=>sum+item,0);
    } else {
        return 1;
    }
}

function perfectNumbers( end, start ){
    start = start || 2;
    var tuples = [];
    if( end > 0 && start < end ){
        for( var i = start; i < end; i++ ){
            var factors = factorize(i);
            tuples.push([i,sumFactors(factors)]);
        }
    }
    return tuples.filter(item=>numberClass(item[0], item[1])===0).map(item=>item[0]);
}

function numberClass( number, properSum ){
    return number - properSum;
}

console.time("factorize");
console.log(perfectNumbers(100000));
console.timeEnd("factorize");

function perfectNumberCandidate(i){
    return 2**(i-1)*(2**i-1);
}

function generateCandidates(limit){
    var result = [];
    for( var i = 0; i < limit; i++ ){
        result.push(perfectNumberCandidate(i));
    }
    return result;
}

console.time("candidateFactorize");
console.log(generateCandidates(10).filter(item=>item>1).map(item=>[item,sumFactors(factorize(item))]).filter(item=>numberClass(item[0], item[1])===0).map(item=>item[0]));
console.timeEnd("candidateFactorize");